It is desirous to have an apparatus capable of measuring cardiac output in a non-invasive way. Several breathing circuits have been employed in the non-invasive measurement of cardiac output ({dot over (Q)}). For example, Gedeon in 1980 described a method of calculating {dot over (Q)} in ventilated patients using the equation
      Q    .    =                              V          .                ⁢                  CO          2                    -                        V          .                ⁢                  CO                      2            ′                                              PETCO                  2          ′                    -              PETCO        2            where PETCO2 and PETCO2′ are the end tidal PCO2 resulting from a change in CO2 elimination from the lung ({dot over (V)}CO2) from {dot over (V)}CO2 to {dot over (V)}CO2′ respectively. To perform the method, a breathing circuit is required that can impose a step change in CO2 elimination in the lungs. The change in {dot over (V)}CO2 is sustained for about one blood recirculation time, or about 30 s. Orr et al. reduced lung CO2 elimination by using a breathing circuit where a dead space is temporarily interposed between the ventilator and the patient's airway resulting in a transient period of rebreathing previously exhaled gas. This is presently the method used by a commercially available product produced by Respironics. Rebreathing previously exhaled gas does not eliminate CO2 from the lung so the CO2 elimination is reduced proportional to the part of the minute ventilation that is constituted by rebreathed gas. The main limitation of the breathing circuits and methods proposed by Gedeon and Orr is that they can only be used in mechanically ventilated patients, as ventilated patients will increase their breath size or breathing frequency to compensate for the reduction in ventilation induced by inhaling the rebreathed gas.